User:Taro Terao

Taro Terao (talk) 05:21, 2 May 2013 (UTC)

$$\log x = \int_1^x \frac{ds}{s}$$

$$4\pi G = c = \varepsilon_0 = \mu_0 = k = h / 2\pi i = 1$$

$$a.\!b.\!c = a.\!b + 2\pi i \times 0.c$$

$$x\ \mathrm{X} = \exp x$$

$$\mathbb{Q} = \varinjlim \mathbb{Z}/s$$

$$\widehat\mathbb{Z} = \varprojlim n\backslash\mathbb{Z} = \prod_p \mathbb{Z}_p$$

$$\mathbb{Z}_p = \varprojlim p^\nu\backslash\mathbb{Z}$$

$$\mathbb{Q}_p = \mathbb{Z}_p \otimes \mathbb{Q}$$

$$\mathbb{A} = \widehat\mathbb{Z} \times \mathbb{R}$$

$$\mathbb{A_Q} = \mathbb{A} \otimes \mathbb{Q}$$

$$n \backslash r / s = (r/s) \otimes \prod_{p \vert n} \mathbb{Q}_p$$

$$x = \operatorname{sgn} x \prod_p p^{\operatorname{ord}_p x} = (\operatorname{sgn}_p x)(\exp_p \log_p x)p^{\operatorname{ord}_p x} = (\operatorname{sgn}_\infty x)(\exp_\infty \operatorname{ord}_\infty x) = \exp_\infty \log_\infty x$$